I have a human body object. I'm creating a new object that conforms to the surface of the body. I'm using "snap to face" to keep new vertices on the faces of the body object. I want to use proportional editing on the new object. Is there a way to keep all vertices attached to the faces? A plugin, perhaps?
Besides all the good suggestions that came so far, what comes closest to your question in my opinion is the project individual option of Blender. You need to set snapping to snap to face first to see the button. Then you can toggle this option on in the 3D Viewport (red square):
Now, all translation tools, move, rotate, scale, even with proportional editing, will snap the whole selection to other faces from the view you're looking at (hold down Ctrl to enable snapping of course):
Quick animation / comparison here:
Retopoflow for the win. It's technically a retopology tool, but its surface snapping tools allow it to do a lot more. This is where I got it. https://cgcookiemarkets.com/all-products/retopoflow/